Measuring the Hubble Constant Using Gravitational Lenses Roger Blandford KIPAC Stanford Sherry Suyu, Phil Marshall, Chris Fassnacht, Tommaso Treu, Leon Koopmans, Matt Auger, Stefan Hilbert, Tony Readhead, Steve Myers, Gabriela Surpi, Frederic Courbin, George Meylan… 22 ii 2011 STScI

22 ii 2011 STScI http://www.slac.stanford.edu/~pjm/lensing/wineglasses

Light “travels slower” Refraction of Light Light travels slower in glass Lens Light travels faster in air Wave crests Light rays Light “travels slower” in glass and is refracted 22 ii 2011 STScI

Deflection of Light Newton: Opticks, Query1: Do not bodies act upon Light at a distance, and by their action bend its rays; and is not this action (caeteris paribus) strongest at the least distance? 22 ii 2011 STScI

Einstein’s General Theory of Relativity 1915: Spacetime is curved around a massive body. Light follows straight lines (geodesics) which appear to be curved. This doubles the effect. 1919: Eclipse measurements confirm that solar deflection is twice Newtonian expectation and makes Einstein a household name. Now measured to 1/1000. 1919: Eddington realizes that relativistic problem just like the Newtonian problem. Light travels slower in a gravitational field 22 ii 2011 STScI Eddington

Clusters of galaxies: a ~ 10 arcsec Surface density ~ 1 g cm-2  Source Lens Observer Stars: a ~ microarcsec Galaxies: a ~ arcsec Clusters of galaxies: a ~ 10 arcsec Surface density ~ 1 g cm-2 22 ii 2011 STScI

Which way shall I go? Light makes the shortest (or the longest) journeys. (Fermat) 22 ii 2011 STScI

Gravitational Lenses and the Hubble Constant  S D H0=V/d ~t -1 2 O Direct measurement Insensitive to world model Lens model dependence STScI 22 ii 2011

Q0957+561 Walsh, Carswell & Weymann (1979) 22 ii 2011 STScI

John Bahcall (1934-2005) Moderated debate between Tammann and van den Berg in 1996 H0 features prominently in “Unsolved Problems” 22 ii 2011 STScI

Standard candles, rulers, timers etc Type Ia supernovae: standard candles Fluctuations in the Cosmic Microwave Background radiation Baryon Acoustic Oscillations in the galaxy clustering power spectrum Periods of Cepheid variable stars in local galaxies Something else? (sound speed x age of universe) subtends ~1 degree gas density fluctuations from CMB era are felt by dark matter - as traced by galaxies in the local(ish) universe 22 ii 2011 STScI

The Measure of the Universe Historically, h= (H0/100 km s-1 Mpc-1) ~ 0.3-~5 10 x Error! Recent determinations: HST KP (Freedman et al) <h>=0.72+/-0.02+/-0.07 Masers (Macri et al) h=0.74+/-0.03+/-0.06 WMAP (Komatsu et al) h=0.71+/-0.025 (FCDM) BAO (Percival et al 2010) h=0.70+/-0.015 (FCDM) Distance Ladder (Riess et al) h=0.74+/-0.04 22 ii 2011 STScI

B1608+656 (Myers, CLASS 1995) Dust 22 ii 2011 STScI

Data Compact radio source (CLASS) Relative magnifications VLBI Astrometry to 0.001” Relative magnifications m A,C,D =2, 1, 0.35 Time delays (Fassnacht) tA,C,D = 31.5, 36, 77 d (+/-1.5) Elliptical galaxy lenses (Fassnacht, Auger) G1: z=0.6304, s=260(+/-15) km s-1; G2 K+A galaxy source (Myers) z=1.394 HST imaging V, I, H bands 22 ii 2011 STScI

Modeling Gravitational Lenses Surface brightness (flux per solid angle) changes along ray ~ a-3 Unchanged by lens Images of same region of source have same surface brightness Complications Deconvolution (HST blurring) Deredenning (dust) Decontamination (source + lens) Image Source 22 ii 2011 STScI

Results H0=71+/-3 km s-1 Mpc-1 Iterative modeling Bayesian analysis Potential residuals ~ 2% Adopt fixed world model Major sensitivity is to zL Assume lens model correct Assume propagation model correct H0=71+/-3 km s-1 Mpc-1 Suyu et al (2010) If relax world model, dh~0.05; If combine with WMAP5 (+flatness), dw~0.2 22 ii 2011 STScI

Limits to the accuracy Lens Model Time delays Mass sheet degeneracy Velocity dispersion Measuring width of ring Time delays Not now limiting accuracy More monitoring Structure along line of sight Distorts images of source and lens Current effort 22 ii 2011 STScI

“Mass-sheet” model degeneracy κext [Courbin et. al. 2002] To break this degeneracy, we need more information about the mass distributions: Stellar dynamics Slope g from arc thickness Structures along the LOS Lens mass, profile slope and line of sight mass distribution are all degenerate: 22 ii 2011 STScI

Geodesic deviation equation Sachs Zel’dovich Feynman Refsdal Gunn Penrose\ Alcock Anderson O x Proper transverse Separation vector q Angle at observer G=c=H0=1 Null geodesic congruence backward from observer Convergence k and shear g First focus, tangent to caustic, multiple imaging Distance measure is affine parameter dxa ~ ka dl where ka is a tangent vector along the geodesic Choose where a =w0/w is the local scale factor errors O(f) relative to homogeneous reference universe For pure convergence, enthalpy density x=d q 22 ii 2011 STScI angular diameter distance

Homogeneous Cosmology For FLCDM universe w=rM No contribution from L Introduce h=x/a, comoving distance, radius dr=dl/a2 and RW line element to obtain Current separation For k=-1, h = qR0sinh (r/R0) 22 ii 2011 STScI

Time delays Single deflector a h Multi-sheet propagation Deviation relative to undeflected ray h Multi-sheet propagation 22 ii 2011 STScI

Inhomogeneous matter distribution Group Galaxy Void <r> rb x Simple Model Background density rb(a) halos modeled by spherical profiles centered on galaxy/group centers amplitude and size scaled to luminosity incorporate bias? NFW better than isothermal Use simulations, GGL to calibrate test convergence and estimate error 22 ii 2011 STScI

Multi-screen Propagation Treat screens as “weak deflectors” Potential: Y ~ L.x+x.Q.x/2+… ; deflections, linear Distort appearance of source and lens Many screens – multiply matrices Model lens in lens plane not on sky 22 ii 2011 STScI

B1608+656: Statistical approach Modeled external shear ~0.1; need k for H0 B1608+656 has twice the average galaxy number density (Fassnacht et al. 2009) Find κext along all LOS in MS that have 2x ‹ngal› Ray-trace through Millennium S Identify LOS where SL occurs Find κext along LOS, excluding the SL plane (Hilbert et al. 2007) 22 ii 2011 STScI

B1608+656-Particular Approach Groups (Fassnacht et al) z=0.265 Off center =>  z=0.63 (G1, G2)  =150+/-60 km s-1 z=0.426, 0.52 Centered lens =>  ~0 Photometry 1500 ACS galaxies over 10sm 1700 P60 galaxies over 100 sm Redshifts 100 zs Experimenting with different prescriptions for assigning halos 22 ii 2011 STScI

Additional Lenses Courbin 22 ii 2011 STScI

Future lens cosmography (Marshall et al) 2010 - 2016: ~3000 new lensed quasars with PS1, DES, HSC About 500 of these systems will be quads A significant monitoring follow-up task! A larger statistical sample of doubles would provided added value, once calibrated by the quads The spectroscopic follow-up is not demanding given rewards Intensive modeling approach seems unavoidable 100 lenses observed to B1608’s level of detail could yield Hubble’s constant to percent precision LSST, WFIRST… 22 ii 2011 STScI

Summary Lens H0 is competitive Promising results with B1608+656 ~4% with strong priors; ~7% after relaxing world model Promising results with B1608+656 h=0.71+/-0.03 with strong priors Limited by understanding of line of sight External convergence and shear New formalism for multi-path propagation Distortion not delay – matrix formalism Observations show overdense line of sight Imaging and spectroscopy Other good candidates Existing and future options 22 ii 2011 STScI

Thanks to: Sherry Suyu, Phil Marshall, Chris Fassnacht, Tommaso Treu, Leon Koopmans, Matt Auger, Stefan Hilbert, Tony Readhead, Steve Myers, Gabriela Surpi, Frederic Courbin, George Meylan… HST John Bahcall 22 ii 2011 STScI